The GW-Universe Toolbox II: constraining the binary black hole population with second and third generation detectors

Abstract

Context:The GW-Universe Toolbox is a software package that simulates observations of the Gravitational Wave (GW) Universe with different types of GW detectors, including Earth-based/Space-borne laser interferometers and Pulsar timing arrays. It is accessible as a website, and can also be imported as a Python module and run locally. Methods: We employ the GW-Universe Toolbox to generate synthetic catalogues of detections of stellar mass binary black hole (BBH) mergers. As an example of its scientific application, we study how GW observations of BBHs can be used to constrain the merger rate as function of redshift and masses. We study advanced LIGO (aLIGO) and Einstein Telescope (ET) as two representatives for the 2nd and 3rd generation GW observatories. We also simulate the observations from a detector that is half as sensitive as the ET in design which represents an early phase of ET. Two methods are used to obtain the constraints on the source population properties from the catalogues: the first assumes a parametric differential merger rate model and applies a Bayesian inference; The other is non-parametric and uses weighted Kernel density estimators. Results: The results show the overwhelming advantages of the 3rd generation detector over the 2nd generation for the study of BBH population properties, especially at a redshifts higher than ∼ 2, where the merger rate is believed to peak. With the LIGO catalogue, the parametric Bayesian method can still give some constraints on the merger rate density and mass function beyond its detecting horizon, while the non-parametric method lose the constraining ability completely there. The difference is due to the extra information placed by assuming a specific parameterisation of the population model in the Bayesian method; While in the non-parametric method, no assumption of the general shape of merger rate density and mass function are placed, not even the assumption of its smoothness. These two methods represent the two extreme situations of general population reconstruction. We also find that, despite the numbers of detection of the half-ET can be easily compatible with full ET after a longer observation duration, the catalogue from the full ET can still give much better constraints on the population properties, due to its smaller uncertainties on the physical parameters of the GW events.